Theorems · Definition · category theory

CategoryTheory.FreeGroupoid.liftNatIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {G : Type u₁} →
      [inst_1 : CategoryTheory.Groupoid G] →
        (F₁ F₂ : CategoryTheory.Functor (CategoryTheory.FreeGroupoid C) G) →
          ((CategoryTheory.FreeGroupoid.of C).comp F₁ ≅ (CategoryTheory.FreeGroupoid.of C).comp F₂) → (F₁ ≅ F₂)

In order to define a natural isomorphism F ≅ G with F G : FreeGroupoid ⥤ D, it suffices to do so after precomposing with FreeGroupoid.of C.

Defined in

Mathlib.CategoryTheory.Groupoid.FreeGroupoidOfCategory

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Groupoid